Flexible coupling with radially offset beams formed by asymmetric slot pairs

ABSTRACT

A flexible coupling for flexibly joining two shafts includes a unitary solid cylindrical body having a first end, a second end, and therebetween having one or more longitudinally spaced circular disks spaced by asymmetric slot pairs; a radially offset beam formed between a first slot and a second slot of each asymmetric slot pair, such that the radially offset beam is parallel to a diameter of the cylindrical body and is offset from the parallel diameter by a radial beam offset distance R 1 ; each beam being rotationally offset from longitudinally adjacent beams; and hub means at the first end for coaxially connecting the first end to a first one of the two shafts, and hub means at the second end for coaxially connecting the second end to a second one of the two shafts.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional PatentApplication No. 60/325,429, filed Sep. 27, 2001 by Dennis G. Berg.

TECHNICAL FIELD OF THE INVENTION

[0002] The present invention relates to a flexible coupling for couplingtwo shafts, and more particularly to a flexible coupling with aslot-formed beam construction.

BACKGROUND OF THE INVENTION

[0003] The use of flexible couplings for interconnecting driving anddriven shafts of precision instruments wherein the coupling is capableof accommodating shaft misalignments and axial shaft movements andpermits limited torsional or radial deflection thereof is well known. Inselected portions of an article entitled “Radial-Beam Couplings: A CutAbove the Rest” (Machine Design; Jul. 6, 2000) John B. Ricker states:“Of the many types available, single piece flexible couplings are theleast expensive, and common geometries include radial slotted beam,helical or spiral, and bellows. The most critical factors to considerwhen choosing flexible couplings include torque capacity, torsionalstiffness, bearing loads, transmission errors, shaft misalignment, andservice life. Torque capacity is a measure of the coupler's amount ofangular or parallel offset allowed from motor to load, and the lifeexpectancy of the coupling. That is, stiff couplings operating underrelatively high stress from large offsets can't survive millions ofoperating cycles. Transmission errors manifest themselves as smallvariations in velocity and position between motor and load. Thevariations are due primarily to coupling geometry and relative size.Bellows couplings usually provide the lowest transmission errors andradial bearing loads, good lateral flexibility, and the highesttorsional stiffness. However, they have lower peak and running torquefor equivalent sizes and are the most expensive. Bellows couplings havebeen traditionally used in smaller stepmotor and servomotor-drivensystems. By comparison, helical or spiral couplings have sufficientlateral flexibility to handle large shaft offsets. But they also haveonly moderate torsional stiffness and the largest transmission errors.Helical couplings are generally categorized by the number of startingslots. For example, a single-beam helical coupling has one continuouscut throughout its entire one-piece flexing or working length. Bycontrast, a six-beam coupling has two sets of three helical cuts 120°apart separated by a center piece. A hub at each end of the couplingconnects the motor drive shaft to the load, or feedback devices such asresolvers and encoders to lead screws and power transmission components.Ordinary radial beam slotted-type couplings fall between the above twotypes for cost, torsional stiffness, and transmission errors (driving anencoder), but produce the highest radial bearing load.”

[0004] An example of a helical flexible coupling is shown by U.S. Pat.No. 4,203,305 (Williams; 1980) which discloses a flexible coupling fortorque transmission having a plurality of helical beams extendingbetween the coupling ends.

[0005] An example of a radial beam slotted-type coupling is shown byU.S. Pat. No. 5,299,980 (Agius; 1994) which discloses a constantvelocity flexible coupling for coupling two shafts that has a solidunitary body (22) with a plurality of complimentary pairs of slots(e.g., 34 paired with 36) positioned between a first and second end(hubs 24, 26). The plurality of complimentary pairs of slots extendinwardly from the circumference of the (cylindrical) body to apredetermined depth so as to form a plurality of beams (e.g., 46)between the complimentary pairs of slots. A plurality of disks (e.g.,111, 112) are formed in the body by the plurality of complementary pairsof slots, and the plurality of beams join and bridge the space betweenadjacent disks. Adjacent beams (e.g., 46, 64 or 78, 84) are angularlyoffset by a number of degrees (e.g., 90 degrees or e.g., 30 degrees).The illustrations (FIGS. 1-16) show that the “complimentary pairs ofslots extending inwardly from the circumference of the body to apredetermined depth” form radial beams that are centered on diameters ofthe cylindrical beam, i.e., the “predetermined depth” is the same foreach of the slots in a “complimentary pair of slots”.

[0006] As stated in the Ricker article hereinabove, radial beamslotted-type couplings fall between the bellows and helical types offlexible couplings in terms of cost, torsional stiffness, radial bearingload, and transmission errors. It is an object of the present inventionto provide a novel flexible coupling that achieves performanceadvantages of both the bellows type and the slotted radial beam typewhile maintaining the low cost advantage of slot and beam types offlexible couplings.

BRIEF SUMMARY OF THE INVENTION

[0007] According to the invention, a flexible coupling for flexiblyjoining two shafts comprises a unitary solid cylindrical body having afirst end, a second end, and therebetween having one or morelongitudinally spaced circular disks spaced by asymmetric slot pairs; aradially offset beam, having a minimum beam thickness T1 and alongitudinal beam length L1, formed between a first slot and a secondslot of each asymmetric slot pair, such that the radially offset beam isparallel to a diameter of the cylindrical body and is offset from theparallel diameter by a radial beam offset distance R1; each beam beingrotationally offset from longitudinally adjacent beams; and hub means atthe first end for coaxially connecting the first end to a first one ofthe two shafts, and hub means at the second end for coaxially connectingthe second end to a second one of the two shafts.

[0008] According to the invention, the radial beam offset distance R1 isat least equal to or greater than a radius R2 of a coaxial shaft hole ofthe hub means at the first end or at the second end.

[0009] According to the invention, a rotational offset angle betweenlongitudinally adjacent beams has the same magnitude for all pairs oflongitudinally adjacent beams; and the rotational offset angle has amagnitude that divides into 360 degrees an integer number N times.Preferably the quantity of beams is an integer multiple of the number N.Also preferably the rotational offset angle increments in the samerotational direction from each beam to each beam's next longitudinallyadjacent beam progressing from a first beam at the first end to a lastbeam at the second end. However, the rotational increment may vary andis not required to be the same.

[0010] According to the invention, all of the disks have a same nominaldisk length (thickness) L3; and all of the first slots and all of thesecond slots have a same nominal slot length L2. Preferably the nominaldisk length L3 is at least equal to, and may be greater than, a minimumvalue of the beam length L1.

[0011] According to the invention, the beam length L1 has a constantvalue for the entire beam.

[0012] According to the invention, the sides of the first slots and thesides of the second slots all have a single valued slot slope angle withrespect to the plane of a radial slot centerline, wherein the slot slopeangle has a value of up to 5 degrees. Preferably the slot slope anglehas a value of up to 2 degrees.

[0013] According to the invention, each beam has a beam thickness thatis uniformly equal to the minimum beam thickness T1 throughout alongitudinal length between adjacent disks.

[0014] According to the invention, each beam has a beam thickness thatvaries along a longitudinal length between adjacent disks, such that theminimum beam thickness T1 occurs in the approximate center of thelongitudinal length, and the beam thickness increases from the minimumthickness T1 to a maximum where the beam joins a disk, with the increasebeing determined by rounded bottoms on the first slot and on the secondslot of the asymmetric slot pair that formed the beam.

[0015] According to the invention, the hub means for coaxiallyconnecting each of the first and second ends to one of the two shaftscomprises a shaft hole with set screws, clamps or other means.

[0016] According to the invention, the two shafts are rotating membershaving potentially different axes of rotation. Alternatively, the twoshafts are structural members that require flexible joining.

[0017] According to the invention, a method of flexibly joining twoshafts with a flexible coupling, comprises the steps of: making theflexible coupling out of a unitary solid cylindrical body having a firstend and a second end; forming a plurality of radially orientedasymmetric slot pairs longitudinally spaced from the first end to thesecond end; forming one or more circular disks longitudinally betweenasymmetric slot pairs; forming a radially offset beam between a firstslot and a second slot of each asymmetric slot pair, such that theradially offset beam is parallel to a diameter of the cylindrical bodyand is offset from the parallel diameter by a radial beam offsetdistance R1; rotationally offsetting each beam from longitudinallyadjacent beams; and providing hub means at the first end for coaxiallyconnecting the first end to a first one of the two shafts, and hub meansat the second end for coaxially connecting the second end to a secondone of the two shafts. The term “unitary” may include inserts affixed toor molded in the body.

[0018] Other objects, features and advantages of the invention willbecome apparent in light of the following description thereof.

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Reference will be made in detail to preferred embodiments of theinvention, examples of which are illustrated in the accompanying drawingfigures. The figures are intended to be illustrative, not limiting.Although the invention is generally described in the context of thesepreferred embodiments, it should be understood that it is not intendedto limit the spirit and scope of the invention to these particularembodiments.

[0020] Certain elements in selected ones of the drawings may beillustrated not-to-scale, for illustrative clarity. The cross-sectionalviews, if any, presented herein may be in the form of “slices”, or“near-sighted” cross-sectional views, omitting certain background lineswhich would otherwise be visible in a true cross-sectional view, forillustrative clarity.

[0021] Elements of the figures can be numbered such that similar(including identical) elements may be referred to with similar numbersin a single drawing. By way of example not related to the presentdescription, each of a plurality of elements collectively referred to as199 may be referred to individually as 199 a, 199 b, 199 c, etc. Or,related but modified elements may have the same number but aredistinguished by primes. By way of example not related to the presentdescription, 199, 199′, and 199″ may be three different elements whichare similar or related in some way, but have significant modifications,e.g., a member 199 having a static imbalance versus a similar butdifferent member 199′ of the same design, but having a couple imbalance.Such relationships, if any, between similar elements in the same ordifferent figures will become apparent throughout the specification,including, if applicable, in the claims and abstract.

[0022] The structure, operation, and advantages of the present preferredembodiment of the invention will become further apparent uponconsideration of the following description taken in conjunction with theaccompanying drawings, wherein:

[0023]FIG. 1 is a side view of a flexible coupling according to theinvention, wherein the visible sides of radially offset beams arespeckled for emphasis;

[0024]FIG. 2 is an exploded perspective view of the flexible coupling ofFIG. 1 showing cross-sections of the beams between successive disks,according to the invention;

[0025]FIG. 3 is an end view of a cross-section through the first(right-hand) beam of FIGS. 1 and 2 showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0026]FIG. 4 is an end view of a cross-section through the second beamfrom the right of FIGS. 1 and 2, showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0027]FIG. 5 is an end view of a cross-section through the third beamfrom the right of FIGS. 1 and 2, showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0028]FIG. 6 is an end view of a cross-section through the fourth beamfrom the right of FIGS. 1 and 2, showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0029]FIG. 7 is an end view of a cross-section through the fifth beamfrom the right of FIGS. 1 and 2, showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0030]FIG. 8 is an end view of a cross-section through the sixth beamfrom the right of FIGS. 1 and 2, showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0031]FIG. 9 is an end view of a cross-section through the seventh beamfrom the right of FIGS. 1 and 2, showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0032]FIG. 10 is an end view of a cross-section through the eighth beamfrom the right of FIGS. 1 and 2, showing radial offset and rotationalangular positioning of the beam, according to the invention;

[0033]FIG. 11 is an end view of a flexible coupling with two beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0034]FIG. 12 is an end view of a flexible coupling with three beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0035]FIG. 13 is an end view of a flexible coupling with four beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0036]FIG. 14 is an end view of a flexible coupling with five beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0037]FIG. 15 is an end view of a flexible coupling with six beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0038]FIG. 16 is an end view of a flexible coupling with seven beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0039]FIG. 17 is an end view of a flexible coupling with eight beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0040]FIG. 18 is an end view of a flexible coupling with nine beamshidden below an end hub, the beams indicated by dashed lines, showingradial offset and rotational angular positioning of the beams, accordingto the invention;

[0041]FIG. 19 is a side cross-sectional view of a beam between portionsof two adjacent disks, showing an embodiment of the flexible couplinghaving sloped sides and rounded ends for the slots paired around thebeam, according to the invention;

[0042]FIG. 19A is a side cross-sectional view of two adjacent beamsbetween portions of three adjacent disks, showing an embodiment of theflexible coupling having sloped sides and rounded ends for the slotspaired around each beam, according to the invention;

[0043]FIG. 20 is a side cross-sectional view of two adjacent beamsbetween portions of three adjacent disks, showing an embodiment of theflexible coupling having non-sloped sides and square ends for the slotspaired around each beam, according to the invention;

[0044]FIG. 21 is the cross-sectional end view of FIG. 3, showingdimensional characteristics of the beam relative to a hub with a shafthole, according to the invention;

[0045]FIG. 21A is the cross-sectional end view of FIG. 4 superimposed onthe view of FIG. 3, showing an angular relationship between the adjacentbeams of the two views, according to the invention;

[0046]FIG. 22 is a perspective view of an embodiment of the flexiblecoupling having shaft hole and set screw means for coaxially connectingthe flexible coupling to shafts, according to the invention; and

[0047]FIG. 23 is a perspective view of an embodiment of the flexiblecoupling having shaft hole and clamp means for coaxially connecting theflexible coupling to shafts, according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0048]FIGS. 1 through 10 (FIGS. 1-10) show a flexible coupling 108 thatis an embodiment of the present invention having eight radially offsetbeams. The flexible coupling 108 has a unitary solid cylindrical body 14with first and second ends 2 a, 2 b that are formed as hubs having means(e.g., coaxial shaft holes 4 a, 4 b) for coaxially connecting each ofthe first and second ends 2 a, 2 b to one of two shafts (not part of theinvention, e.g., shafts 901, 903 outlined in FIG. 22) that are to beflexibly joined by the flexible coupling 108. One or more circular disks6 a, 6 b, 6 c, 6 d, 6 e, 6 f, 6 g (collectively referred to as disks 6)are longitudinally spaced between the first and second ends 2 a, 2 b byasymmetric pairs of slots 10 a/11 a, 10 b/11 b, 10 c/11 c, 10 d/11 d, 10e/11 e, 10 f/11 f, 10 g/11 g, 10 h/11 h (asymmetric slot pairs 10/11)forming radially offset beams 8 a, 8 b, 8 c, 8 d, 8 e, 8 f, 8 g, 8 h(collectively referred to as beams 8) therebetween. An axis ofrevolution AR for the cylindrical body 14 is shown extending through thelength of the coupling 108. The shaft holes 4 a, 4 b, which areoptionally of different diameters, are both coaxial to the axis ofrevolution AR and either shaft hole 4 a, 4 b optionally extends onlythrough a corresponding end 2 a, 2 b, respectively, as shown, oroptionally extends through at least some of the disks 6 and beams 8.

[0049] Referring to FIGS. 1, 2, and 3: longitudinally between a firstend 2 a and a first disk 6 a, a first beam 8 a is formed between a firstdeep slot 10 a and a first shallow slot 11 a (a first asymmetric slotpair 10 a/11 a). Referring to FIGS. 1, 2, and 4: longitudinally betweenthe first disk 6 a and a second disk 6 b, a second beam 8 b is formedbetween a second deep slot 10 b and a second shallow slot 11 b (a secondasymmetric slot pair 10 b/11 b). Referring to FIGS. 1, 2, and 5:longitudinally between the second disk 6 b and a third disk 6 c, a thirdbeam 8 c is formed between a third deep slot 10 c and a third shallowslot 11 c (a third asymmetric slot pair 10 c/11 c). Referring to FIGS.1, 2, and 6: longitudinally between the third disk 6 c and a fourth disk6 d, a fourth beam 8 d is formed between a fourth deep slot 10 d and afourth shallow slot 11 d (a fourth asymmetric slot pair 10 d/11 d).Referring to FIGS. 1, 2, and 7: longitudinally between the fourth disk 6d and a fifth disk 6 e, a fifth beam 8 e is formed between a fifth deepslot 10 e and a fifth shallow slot 11 e (a fifth asymmetric slot pair 10e/11 e). Referring to FIGS. 1, 2, and 8: longitudinally between thefifth disk 6 e and a sixth disk 6 f, a sixth beam 8 f is formed betweena sixth deep slot 10 f and a sixth shallow slot 11 f (a sixth asymmetricslot pair 10 f/11 f). Referring to FIGS. 1, 2, and 9: longitudinallybetween the sixth disk 6 f and a seventh disk 6 g, a seventh beam 8 g isformed between a seventh deep slot 10 g and a seventh shallow slot 11 g(a seventh asymmetric slot pair 10 g/11 g). Referring to FIGS. 1, 2, and10: longitudinally between the seventh disk 6 g and a second end 2 b, aneighth beam 8 h is formed between an eighth deep slot 10 h and an eighthshallow slot 11 h (an eighth asymmetric slot pair 10 h/11 h).

[0050] An important feature of the present invention is a radial offsetdesign for the beams 8. Referring to FIG. 21, various dimensions areshown for a view comparable to the cross-sectional views of FIGS. 3-10,but most closely representing the view of FIG. 3. The first beam 8 a isformed between the first deep slot 10 a and the first shallow slot 11 a,such that the first beam 8 a has a beam thickness T1. A beam centerlineCL1 delineates the center of the beam thickness T1 along the entirelength of the first beam 8 a. As shown in FIG. 21 for the first beam 8a, typical of all the beams 8, the first beam 8 a (i.e., the beamcenterline CL1) is parallel to a diameter DM of the cylindrical body 14,a portion of which is illustrated by the first end 2 a. Furthermore, theradially offset beam 8 (e.g., first beam 8 a) is offset from theparallel diameter DM by a non-zero radial beam offset distance R1. Thusthe asymmetric slot pair 10/11 (e.g., first asymmetric slot pair 10 a/11a) comprises a first deep slot 10 a with a deep slot depth D2 and afirst shallow slot 11 a with a shallow slot depth D1 such that the deepslot depth D2 is greater than the shallow slot depth D1, preferablysignificantly greater. In a preferred embodiment illustrated by FIG. 21,the radial beam offset distance R1 is equal to a shaft hole radius R2being the radius of at least one of the shaft holes 4 (e.g., 4 a). Theslot depths D1 and D2 are measured from the beam 8 to an outer peripheryof the body 14 along a diameter of the body 14 that is perpendicular tothe beam 8 formed between the slots 11 and 10. Thus the slot depths D1and D2 represent the greatest distance through the slots 11 and 10,respectively, measured perpendicularly from the beam 8 to the peripheryof the body 14.

[0051] Compared to prior art radial beam designs, the radially offsetbeam design maintains excellent torsional and longitudinal stiffness,while enabling improved longitudinal bending flexibility foraccommodating joined shafts that have angular and/or parallelmisalignment. Each deep slot 10 is able to open wider since its pairedshallow slot 11 pinches together much more due to a short pivot armlength D1. It can be seen that the radial beam design of the prior art,wherein the paired slot depths are equal and slightly less than theradius of the coupling, limits the amount of longitudinal flexing for acoupling with the same diameter as the present invention due to arelatively longer pivot arm length in any slot being pinched together.

[0052] As is readily apparent from the drawings, especially FIGS. 3-10,each beam 8 is rotationally offset from any adjacent beam. Referring toFIGS. 21 and 3, the first beam 8 a is positioned at a first rotationalangle α relative to an arbitrary axis labeled “x” that is orthogonal toan axis of rotation AR of the end hub 2 a. The axis of rotation AR istherefore also the axis of rotation of both ends 2, of all disks 6, andof the cylindrical body 14 of the flexible coupling 108 as shown inFIGS. 1 and 2. From FIG. 4 it can be seen that the next adjacent beam,the second beam 8 b, is rotated clockwise to a second rotational angleα′ (not shown). Likewise, from FIG. 5 it can be seen that the nextadjacent beam, the third beam 8 c, is rotated clockwise to a thirdrotational angle α41 (not shown). The rotation of the beams 8 continuesfrom each beam to each adjacent beam. The difference in rotationalangles α between adjacent beams 8 is a rotational offset angle β. FIG.21A illustrates an example of the rotational offset angle β shownbetween the first beam 8 a and the adjacent second beam 8 b. Since thebeams 8 are radially offset, it is convenient to measure the rotationaloffset angle β between diameters DMa and DMb that are parallel to thebeams 8 a and 8 b, respectively. For the sake of uniformity in flexingas the coupling 108 is rotated, preferably the rotational offset angle βhas the same magnitude for all of the adjacent beams 8 such that therotational offset angle β has a magnitude that divides into 360° aninteger number N times. Most preferably, the number of beams is aninteger multiple of the number N. Also preferably the rotational offsetangle β increments in the same rotational direction as measured from thefirst beam 8 a to the adjacent second beam 8 b, from the second beam 8 bto the adjacent third beam 8 c, and so on from each beam to its nextadjacent beam progressing from the first beam (e.g., first beam 8 a) toa last beam (e.g., eighth beam 8 h). For example, the flexible coupling108 has eight radially offset beams 8 having a single rotational offsetangle β of 45°, which is 360° divided by the integer number N=8. Forexample, the preferred design rules would also be satisfied if therewere two times eight beams 8 (16 beams) having a rotational offset angleβ of 45°, which is 360° divided by eight, resulting in a flexiblecoupling that has twice the flexible length of the flexible coupling108.

[0053] A variety of flexible couplings can be constructed according tothe present invention. FIGS. 11 through 18 (FIGS. 11-18) illustratedesigns having from two beams 8 to nine beams 8. The designs in FIGS.11-18 are only examples, since any number of beams 8 is possible. Eachof the FIGS. 11-18 shows an end view of a coupling wherein theunderlying beams 8 are shown with dashed lines indicating that the beams8 are hidden under an end hub 2 having a shaft hole 4. FIG. 11 shows acoupling 102 having two beams 8 a, 8 b that are uniformly rotationallyoffset by a rotational offset angle β of magnitude 180° (360° divided by2). FIG. 12 shows a coupling 103 having three beams 8 a, 8 b, 8 c thatare uniformly rotationally offset by a rotational offset angle β ofmagnitude 120° (360° divided by 3). FIG. 13 shows a coupling 104 havingfour beams 8 a, 8 b, 8 c, 8 d that are uniformly rotationally offset bya rotational offset angle β of magnitude 90° (360° divided by 4). FIG.14 shows a coupling 105 having five beams 8 a, 8 b, 8 c, 8 d, 8 e thatare uniformly rotationally offset by a rotational offset angle β ofmagnitude 72° (360° divided by 5). FIG. 15 shows a coupling 106 havingsix beams 8 a, 8 b, 8 c, 8 d, 8 e, 8 f that are uniformly rotationallyoffset by a rotational offset angle β of magnitude 60° (360° divided by6). FIG. 16 shows a coupling 107 having seven beams 8 a, 8 b, 8 c, 8 d,8 e, 8 f, 8 g that are uniformly rotationally offset by a rotationaloffset angle β of magnitude 51.4° (360° divided by 7). FIG. 17 shows acoupling 108 (equivalent to the coupling 108 shown in FIGS. 1 and 2)having eight beams 8 a, 8 b, 8 c, 8 d, 8 e, 8 f, 8 g, 8 h that areuniformly rotationally offset by a rotational offset angle β ofmagnitude 45° (360° divided by 8). FIG. 18 shows a coupling 109 havingnine beams 8 a, 8 b, 8 c, 8 d, 8 e, 8 f, 8 g, 8 h, 8 i that areuniformly rotationally offset by a rotational offset angle β ofmagnitude 40° (360° divided by 9).

[0054] Increasing the number of beams 8 produces increasingly flexiblecouplings. A smaller rotational offset angle β between adjacent beams 8results in a smoother transition for the torsional loading of adjacentbeams. For example, the coupling 109 having nine beams 8 with a 40°rotational offset angle β, is much more longitudinally flexible than thecoupling 102 having only two beams 8 with a 180° rotational offset angleβ.

[0055] It is within the scope of the present invention to have differentcross-sectional profiles for the slots 10, 11. For illustrativesimplicity, the views of FIGS. 1 through 18 and 21 and 21A showsquared-off profiles for the slots 10, 11. For example, thecross-sectional view of FIG. 20 shows a portion of the coupling 108 witha squared-off profile. The deep slots 10 (e.g., 10 b,10 c) each havestraight (non-sloping) sides 120, and the paired shallow slots 11 (e.g.,11 b, 11 c) each have straight (non-sloping) sides 121. The beams 8(e.g., 8 b, 8 c) each have a beam length L1 (nominal beam length L1)measured longitudinally between adjacent disks 6 (e.g., disk 6 a to disk6 b, or disk 6 b to disk 6 c); and the beam length L1 is constant forthe entire beam 8 (e.g., 8 b, 8 c). The beams 8 (e.g., 8 b, 8 c) eachhave a beam thickness T1 measured between bottoms of paired slots 10/11(e.g., bottom of shallow slot 11 b to bottom of deep slot 10 b, orbottom of deep slot 10 c to bottom of shallow slot 11 c); and the beamthickness T1 is constant for the entire beam 8 (e.g., 8 b, 8 c).Measured at an outer periphery of the coupling 108, the deep slots 10(e.g., 10 b, 10 c) each have a length L4 that is constant for the entiredeep slot 10, and therefore equals the beam length L1. Also measured atan outer periphery of the coupling 108, the shallow slots 11 (e.g., 11b, 11 c) each have a length L2 that is constant for the entire shallowslot 11, and therefore equals the beam length L1 and thus the deep slotlength L4. Finally, measured at the axis of revolution AR, the disks 6(e.g., disk 6 b) each have a length L3 (nominal disk length L3) that isconstant for the entire disk 6.

[0056] The disk length L3, beam length L1 (equaling slot lengths L2,L4), slot depths D1, D2, and beam thickness T1 can be adjusted to matchphysical characteristics (e.g., bending stress limit) of the materialused for the body 14 with physical demands (e.g., shaft misalignmentangle) of an application for the coupling 108. Preferably the coupling108 has a disk length L3 that is equal to the beam length L1 (and slotlengths L2, L4), and that is also equal to the beam thickness T1.

[0057] A preferred cross-sectional profile for slots 410, 411 (compareslots 10, 11) is illustrated in FIGS. 19 and 19A which showcross-sectional views of portions of a preferred sloped-slot design fora flexible coupling 108′ (compare 108). The deep slots 410 (e.g., 410 b,410 c) each have sides 420 that slope with a slot slope angle φ (openingoutward as measured from a slot centerline CL2 to the deep slot side420), preferably from 0° to 5°, and most preferably from 0° to 2°.Likewise, the paired shallow slots 411 (e.g., 411 b, 411 c) each havesides 421 that slope with a slot slope angle φ (opening outward asmeasured from the slot centerline CL2 to the shallow slot side 421),preferably from 0° to 5°, and most preferably from 0° to 2°. Alsopreferably, the slot slope angle φ has the same magnitude for the deepslots 410 and for the shallow slots 411.

[0058] In its simplest form, parallel-sided slots 410/411 open outwardwith the planes of a plurality of slot slope angles φ all being orientednormal to the entire beam 408, i.e., normal to all points of the beamcenterline CL1 (see both FIGS. 19 and 21). However, it is within thescope of the present invention to have fan-sloped slots 410/411 whereinthe slot slope angle φ is oriented in a plurality of planes that fanaround like radii from a point at the intersection of the beamcenterline CL1 and a diameter DMx that is normal to the beam centerlineCL1.

[0059] An optional, but preferred profile for the sloped slots 410/411includes slot bottoms 430/431 that are rounded with a radius ofcurvature RC1.

[0060] The beams 408 (e.g., 408 b, 408 c) each have a beam length L1between adjacent disks 406 (e.g., disk 406 a to disk 406 b, or disk 406b to disk 406 c) that is measured longitudinally through a beamcenterline CL1. The beams 408 (e.g., 408 b, 408 c) each have a beamthickness T1 measured along the slot centerline CL2 between bottoms(optionally rounded bottoms 430/431) of paired slots 410/411 (e.g.,bottom of shallow slot 411 b to bottom of deep slot 410 b, or bottom ofdeep slot 410 c to bottom of shallow slot 411 c). If the bottoms of theslots 410/411 are flat, then the beam thickness T1 is constant for theentire beam 408; but if the rounded bottoms 430/431 are used, then thebeam thickness T1 varies along the length L1 of the beam 408 (e.g., 408b, 408 c), and has a minimum beam thickness T1 at the slot centerlineCL2. If parallel-sided slots 410/411 are used, then the beam length L1is constant for the entire beam 408; but if fan-sloped slots 410/411 areused, then the beam length L1 varies along the entire beam 408, having aminimum beam length L1 at the point at the intersection of the beamcenterline CL1 and the diameter DMx.

[0061] Measured at an outer periphery of the coupling 108′, the deepslots 410 (e.g., 410 b, 410 c) each have a length L4, and a depth D2measured along the diameter DMx that is normal to the beam centerlineCL1. If parallel-sided slots 410/411 are used 9 see FIG. 20), then thedeep slot length L4 is constant around the periphery of the deep slots410; but if fan-sloped slots 410/411 are used (see FIGS. 19 and 19A),then the deep slot length L4 varies around the periphery of the deepslots 410.

[0062] Also measured at an outer periphery of the coupling 108′, theshallow slots 411 (e.g., 411 b, 411 c) each have a length L2, and adepth D1 measured along the diameter DMx that is normal to the beamcenterline CL1. If parallel-sided slots 410/411 are used, then theshallow slot length L2 is constant around the periphery of the shallowslots 411; but if fan-sloped slots 410/411 are used, then the shallowslot length L2 varies around the periphery of the shallow slots 411. Asa result of the slot slope angle φ being preferably equal for the deepslots 410 and for the shallow slots 411, it can be seen that a slotlength measured at a shallow slot depth D1 in the deep slot 410 willhave the same magnitude as the shallow slot length L2, therefore thelength L2 can also be a “nominal slot length L2” that is used toindicate a longitudinal length for all slots 10 and 11, i.e., for boththe deep slots 10 and the shallow slots 11, regardless of slot profile.

[0063] Finally, measured at the axis of revolution AR, the disks 406(e.g., disk 406 b) each have a nominal disk length L3. As detailedhereinabove, the longitudinal length at any given location on a disk 406is generally variable and is highly dependent on the magnitude of theslot slope angle φ and on the orientation of the plane of the slot slopeangle φ where it passes through the given location.

[0064] The nominal disk length L3, beam length L1, slot lengths L2, L4,slot depths D1, D2, beam thickness T1, slot slope angle φ and choice ofparallel-sided or fan-sloped slots can be adjusted to match physicalcharacteristics (e.g., bending stress limit) of the material used forthe body 414 with physical demands (e.g., shaft misalignment angle) ofan application for the coupling 108′.

[0065] With reference to FIGS. 22 and 23, the two shafts (not part ofthe invention, e.g., 901, 903) that are to be flexibly joined by aflexible coupling 208, 308 (compare 108 and 108′) are fitted intosuitably sized shaft holes 204, 304 (e.g., 204 a, 304 a, compare 4 a, 4b). One shaft hole 204 (e.g., 204 a) is coaxially formed in each end 202a, 202 b of the coupling 208, the ends 202 a, 202 b being hubs havingmeans for coaxially connecting each of the ends 202 a, 202 b to arespective one of the two shafts 901, 903. One shaft hole 304 (e.g., 304a) is coaxially formed in each end 302 a, 302 b of the coupling 308, theends 302 a, 302 b being hubs having means for coaxially connecting eachof the ends 302 a, 302 b to a respective one of the two shafts 901, 903.The suitably sized holes 204, 304 have cross-sectional profiles that fitthe dimensions and shape of the cross-sectional profiles of therespective shaft 901, 903. For example, the cross-sectional profiles canbe circular (as shown) with diameters that may or may not be the samefor the two shafts 901, 903. For example, the cross-sectional profilescan be D-shaped or hexagonal.

[0066]FIG. 22 illustrates a first preferred means for coaxiallyconnecting each of the ends 202 a, 202 b to a respective one of the twoshafts 901, 903 using one or more set screws 252 screwed intocorresponding threaded set screw holes 250 such that the one or more setscrews 252 in an end (e.g., 202 a) press into the shaft (e.g., 901)fitted into the respective shaft hole (e.g., 204 a).

[0067]FIG. 23 illustrates a second preferred means for coaxiallyconnecting each of the ends 302 a, 302 b to a respective one of the twoshafts 901, 903 using clamps 360 a, 360 b, respectively. The clamps 360a, 360 b each comprise a radial clamping slit 356 a, 356 b that dividesa first clamp side 354 a, 354 b from a second clamp side 358 a, 358 b.The clamping slit 356 a, 356 b must not be crossed by a beam in order toassure that at least one of the first and second clamp sides (354 a and358 a, or 354 b and 358 b) is free to move against the other, therebyclamping the shaft 901, 903 in its respective end hub 302 a, 302 b. Theclamping action is accomplished, for example, by a screw 352 in a hole350 that is threaded only in the first clamp side 354 a, 354 b.

[0068] Any suitable material can be used for the body (e.g., 14) of theflexible couplings (e.g., 108) according to the present invention, butpreferably the material is low density (for light weight, low inertia),and resistant to ultraviolet/moisture/oil/fuel/solvent. For example,preferred suitable materials are high performance aluminum alloys orengineered plastics. Use of engineered plastics adds the advantage ofbeing electrically nonconductive.

[0069] Although the invention has been illustrated and described indetail in the drawings and foregoing description, the same is to beconsidered as illustrative and not restrictive in character—it beingunderstood that only preferred embodiments have been shown anddescribed, and that all changes and modifications that come within thespirit of the invention are desired to be protected. Undoubtedly, manyother “variations” on the “themes” set forth hereinabove will occur toone having ordinary skill in the art to which the present invention mostnearly pertains, and such variations are intended to be within the scopeof the invention, as disclosed herein.

What is claimed is:
 1. A flexible coupling for flexibly joining twoshafts, the flexible coupling comprising: a unitary solid cylindricalbody having a first end, a second end, and therebetween having one ormore longitudinally spaced circular disks spaced by asymmetric slotpairs; a radially offset beam, having a minimum beam thickness T1 and alongitudinal beam length L1, formed between a first slot and a secondslot of each asymmetric slot pair, such that the radially offset beam isparallel to a diameter of the cylindrical body and is offset from theparallel diameter by a radial beam offset distance R1; each beam beingrotationally offset from longitudinally adjacent beams; and means at thefirst end for coaxially connecting the first end to a first one of thetwo shafts, and means at the second end for coaxially connecting thesecond end to a second one of the two shafts.
 2. The flexible couplingof claim 1, wherein: the radial beam offset distance R1 is approximatelyequal to the largest of a radius R2 of a coaxial shaft hole of the meansat the first end or at the second end.
 3. The flexible coupling of claim1, wherein: a rotational offset angle between longitudinally adjacentbeams has the same magnitude for all pairs of longitudinally adjacentbeams; and the rotational offset angle has a magnitude that divides into360 degrees an integer number N times.
 4. The flexible coupling of claim3, wherein: the quantity of beams is an integer multiple of the numberN.
 5. The flexible coupling of claim 3, wherein: the rotational offsetangle increments in the same rotational direction from each beam to eachbeam's next longitudinally adjacent beam progressing from a first beamat the first end to a last beam at the second end.
 6. The flexiblecoupling of claim 1, wherein: all of the disks have a same nominal disklength L3; and all of the first slots and all of the second slots have asame nominal slot length L2.
 7. The flexible coupling of claim 6,wherein: the nominal disk length L3 is equal to the nominal slot lengthL2.
 8. The flexible coupling of claim 6, wherein: the nominal disklength L3 is equal to a minimum value of the beam length L1.
 9. Theflexible coupling of claim 1, wherein: the beam length L1 has a constantvalue for the entire beam.
 10. The flexible coupling of claim 1,wherein: the sides of the first slots and the sides of the second slotsall have a single valued slot slope angle with respect to the plane of aradial slot centerline, wherein the slot slope angle has a value of upto 5 degrees.
 11. The flexible coupling of claim 10, wherein: the slotslope angle has a value of up to 2 degrees.
 12. The flexible coupling ofclaim 1, wherein: each beam has a beam thickness that is uniformly equalto the minimum beam thickness T1 throughout a longitudinal lengthbetween adjacent disks.
 13. The flexible coupling of claim 1, wherein:each beam has a beam thickness that varies along a longitudinal lengthbetween adjacent disks, such that the minimum beam thickness T1 occursin the approximate center of the longitudinal length, and the beamthickness increases from the minimum thickness T1 to a maximum where thebeam joins a disk, with the increase being determined by rounded bottomson the first slot and on the second slot of the asymmetric slot pairthat formed the beam.
 14. The flexible coupling of claim 1, wherein: themeans for coaxially connecting each of the first and second ends to oneof the two shafts comprises hub means.
 15. The flexible coupling ofclaim 1, wherein: the means for coaxially connecting each of the firstand second ends to one of the two shafts comprises hub means with ashaft hole with at least one set screw.
 16. The flexible coupling ofclaim 1, wherein: the means for coaxially connecting each of the firstand second ends to one of the two shafts comprises hub means with ashaft hole and at least one clamp.
 17. The flexible coupling of claim 1,wherein: the two shafts are rotating members having potentiallydifferent axes of rotation.
 18. The flexible coupling of claim 1,wherein: the two shafts are structural members that require flexiblejoining.
 19. A method of flexibly joining two shafts with a flexiblecoupling, comprising the steps of: making the flexible coupling out of aunitary solid cylindrical body having a first end and a second end;forming a plurality of radially oriented asymmetric slot pairslongitudinally spaced from the first end to the second end; forming oneor more circular disks longitudinally between asymmetric slot pairs;forming a radially offset beam between a first slot and a second slot ofeach asymmetric slot pair, such that the radially offset beam isparallel to a diameter of the cylindrical body and is offset from theparallel diameter by a radial beam offset distance R1; rotationallyoffsetting each beam from longitudinally adjacent beams; and providingmeans at the first end for coaxially connecting the first end to a firstone of the two shafts, and means at the second end for coaxiallyconnecting the second end to a second one of the two shafts.